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We survey the main results presented in the authors Ph.D Thesis (Monaci 2001), discussed on January 2002 at the University of Bologna (Italy) and supervised by Paolo Toth and Silvano Martello. The thesis deals with exact and heuristic approaches for solving a class of combinatorial optimization problems, with particular emphasis on Two-Dimensional Packing problems and Scheduling problems.

ABS methods are a large class of methods, based upon the Egervary rank reducing algebraic process, first introduced in 1984 by Abaffy, Broyden and Spedicato for solving linear algebraic systems, and later extended to nonlinear algebraic equations, to optimization problems and other fields; software based upon ABS methods is now under development. Current ABS literature consists of about 400 papers...

The Two-Dimensional Finite Bin Packing Problem (2BP) consists of determining the minimum number of large identical rectangles, bins, that are required for allocating without overlapping a given set of rectangular items. The items are allocated into a bin with their edges always parallel or orthogonal to the bin edges. The problem is strongly NP-hard and finds many practical applications. In this paper...

Lagrangian relaxation is usually considered in the combinatorial optimization community as a mere technique, sometimes useful to compute bounds. It is actually a very general method, inevitable as soon as one bounds optimal values, relaxes constraints, convexifies sets, generates columns etc. In this paper we review this method, from both points of view of theory (to dualize a given problem) and algorithms...

In the chemical community the need for representing chemical structures within a given family and of efficiently enumerating these structures suggested the use of computers and the implementation of fast enumeration algorithms. This paper considers the isomeric acyclic structures focusing on the enumeration of the alkane molecular family. For this family, Trinajsti etal. (1991) devised an enumeration...

New upper bounds for the independence number and for the clique covering number of a graph are given in terms of the rank, respectively the eigenvalues, of the adjacency matrix. We formulate a conjecture concerning an upper bound of the clique covering number. This upper bound is related to an old conjecture of Alan J. Hoffman which is shown to be false. Key words: adjacency matrix, eigenvalues, independence...

Algebraic modelling languages allow models to be implemented in such a way that they can easily be understood and modified. They are therefore a working environment commonly used by practitioners in Operations Research. Having once developed models, they need to be integrated inside the company information system. This step often involves embedding a model into a programming language environment:...

We summarize the main results of the authors PhD thesis, defended in February 2003 at the Katholieke Universiteit Leuven (Belgium) and supervised by Dirk Cattrysse. The thesis is written in English and presents a number of solution and modeling approaches for distribution problems in the context of arc routing. In particular, the focus is on (1) local search procedures for arc routing problems, (2)...

This paper addresses a coordination problem concerning two production agents in a manufacturing system. The two agents have a set of processes which must be carried out on some common resource. They can use the resource individually, but in general there may be an overall advantage in concurrently performing certain processes. The problem is to select concurrent processes and to sequence them with...

Yens algorithm is a classical algorithm for ranking the K shortest loopless paths between a pair of nodes in a network. In this paper an implementation of Yens algorithm is presented. Both the original algorithm and this implementation present computational complexity order when considering a worst-case analysis. However, computational experiments are reported, which allow...

The Dial-a-Ride Problem (DARP) consists of designing vehicle routes and schedules for n users who specify pick-up and drop-off requests between origins and destinations. The aim is to plan a set of m minimum cost vehicle routes capable of accommodating as many users as possible, under a set of constraints. The most common example arises in door-to-door transportation for elderly or disabled people...

This paper is the second of a two part series and describes new lower and upper bounds for a more general version of the Two-Dimensional Finite Bin Packing Problem (2BP) than the one considered in Part I (see Boschetti and Mingozzi 2002). With each item is associated an input parameter specifying if it has a fixed orientation or it can be rotated by . This problem contains as special cases...

In bottleneck combinatorial problems, admissible solutions are compared with respect to their maximal elements. In such problems, one may work with an ordinal evaluation scale instead of a numerical scale. We consider here a generalization of this problem in which one only has a partially ordered scale (instead of a completely ordered scale). After the introduction of a mappimax comparison operator...

A survey of the results described in the authors PhD thesis (Montemanni 2001) is presented. The thesis, which was supervised by Prof. Derek H. Smith and Dr. Stuart M. Allen, has been defended in January 2002 at the University of Glamorgan (U.K.). The thesis proposes new heuristic algorithms, based on well-known meta-heuristic paradigms, and new lower bounding techniques, based on linear programming,...

In this paper a variant of Murtys algorithm for ranking assignments according to cost is presented. It is shown that the worst-case computational complexity is better in this variant than in the original form of the algorithm. Computational results comparing three methods for ranking assignments are reported. They show that the behaviour of the new variant is also better in practice.

Given an integer polyhedron , an integer point , and a point , the primal separation problem is the problem of finding a linear inequality which is valid for PI, violated by x*, and satisfied at equality by . The primal separation problem plays a key role in the primal approach to integer programming. In this paper...

In this survey we attempt to give a unified presentation of a variety of results on the lifting of valid inequalities, as well as a standard procedure combining mixed integer rounding with lifting for the development of strong valid inequalities for knapsack and single node flow sets. Our hope is that the latter can be used in practice to generate cutting planes for mixed integer programs. The survey...

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